Electrical Engineering ⇒ Topic : Inductive Coupling in Parallel

INDUCTIVE COUPLING IN PARALLEL:-

When two coils are coupled in parallel and mutual inductance exists, the equivalent inductance of the parallel combination can be calculated in the two cases, i.e., parallel aiding and parallel opposing as follows

(1) parallel aiding

figure (a) shows the connection of parallel connection of two coils where the flux is additive as per dot convention. using kvl, we can write

                                figure (a)  inductive coupling in parellel

                                 ..............  (1)

                                  .............. (2)

from eqs. (1) and (2), we get

                                                    ..............    (3)

here                                                          .................. (4)

using eq. (4), we can write eq. (3), as

                      ...............          (5)

                                                                  ...............         (6)

                                                                  ...................  (7)

using eqs. (6) and (7), we get the following from eq. (1):

       ..............   (8)

if l is the equivalent inductance of the parallel combination, we have:

                                                                                                        .............  (9)    

from eqs. (8) and (9), we can write

                                                                      ............... (10)

equation (10) gives the equivalent inductance of figure (a).

(2) Parallel Opposing:-

Figure (a)shows that the two coils are connected in parallel connection such that mutually induced e.m.f. in one coil due to variation of current in other coil is negative.Using KVL, we can write

                Figure (a) Inductive coupling in parallel (flux opposing

                                                                  ............  (1)

                                                                   ............. (2)

From Eqs. (1) and (2), we have

                                       ............ (3)

 since                                        ............. (4)

Using Eq. (4), we get the following from Eq. (3):

                          .......... (5)

Similarly, we have

                                                              ...............(6)

Using Eqs. (5) and (6), we can write the following from Eq. (1),

         ................. (7)

if L is the equivalent inductance of Figure (a), we can write

                                                                                    ............... (8)

From Eqs. (7) and (8), we get

                                                               .............  (9)

Equation (9) gives the equivalent inductance of Figure (a).